Brand, a two-time All-Star, retired last October. He played five of his 17 NBA seasons with the Sixers, including his final season, 2015-16, when he appeared in 17 games.
"We are thrilled that Elton has agreed to take on the GM position of the Sevens, a natural next step given both his personal and professional skillset," 76ers president of basketball operations Bryan Colangelo said in a statement.
"The transition from a terrific playing career to team management was something that we have been talking about for some time and this opportunity is both timely and appropriate. I look forward to working side-by-side with Elton as we continue to grow and develop our overall basketball program."
Brand, 38, was a consultant for the Sixers last season, focusing on player development.
"I look forward to building upon the successes the Sevens have had both on the court and in the community in Delaware," Brand said in the statement.
Brand averaged 15.9 points and 8.5 rebounds in 1,058 games with the Bulls, Clippers, Mavericks, Hawks and Sixers.
Brand's first four seasons with the Sixers came after he spurned better offers to sign a five-year, $82 million contract with Philadelphia in 2008. The Sixers waived him in 2012.